1. **Stating the problem:** We have a study with 500 males and 500 females (total 1000 participants). The overall vegetarian rate is 2%, so total vegetarians = $1000 \times 0.02 = 20$. Among those with diabetes, the vegetarian rate is 1%. There are equal numbers of male and female vegetarians. We want to analyze the truth of two statements: (I) Sex is not a confounder. (II) Being vegetarian is positively associated with not having diabetes. 2. **Understanding confounding:** A confounder is a variable that is associated with both the exposure (vegetarian diet) and the outcome (diabetes). Since males and females are equally represented among vegetarians, sex is not associated with vegetarian status. Therefore, sex cannot confound the association between vegetarian diet and diabetes. 3. **Association between vegetarian diet and diabetes:** - Overall vegetarian rate: 2% (20 vegetarians). - Vegetarian rate among diabetics: 1%. This means vegetarians are less common among diabetics than in the general study population. 4. **Calculating association:** Let $D$ = having diabetes, $V$ = being vegetarian. We have: $$P(V) = 0.02$$ $$P(V|D) = 0.01$$ Since $P(V|D) < P(V)$, vegetarianism is negatively associated with diabetes. Equivalently, being vegetarian is positively associated with not having diabetes. 5. **Conclusion:** - Statement (I) is true: sex is not a confounder. - Statement (II) is true: being vegetarian is positively associated with not having diabetes. **Final answer:** Both (I) and (II) must be true.